The end of last week saw the carbon concentrations in the atmosphere finally pass the 400-part-per-million threshold. That means carbon levels are higher now than they’ve been for at least 800,000 years, and most likely far longer. There’s nothing special per se about 400 parts per million — other than giving all of us a change to note it in article like this one — but it’s a reminder that we are headed very fast into a very uncertain future.

Parts per million and global temperature change, though, are just numbers. What matters is the effect they will have on life — ours, of course, but also everything else that lives on the planet earth. I’ve written before that while I certainly worry and fear the impact that unchecked climate change will have on humanity, I also feel relatively — relatively — confident that we will, in some ways, muddle through. Human beings have already proved that they are extremely adaptable, living — with various degrees of success — from the hottest desert to the coldest corner of the Arctic. I don’t think a future where temperatures are 4˚F or 5˚F or 6˚F warmer on average will be an optimal one for humanity, to say the least. But I don’t think it will be the end of our species either. (I’ve always favored asteroids for that.)

But the plants and animals that share this planet with us are a different story. Even before climate change has really kicked in, human expansion had led to the destruction of habitat on land and in the sea, as we crowd out other species. By some estimates we’re already in the midst of the sixth great extinction wave, one that’s largely human caused, with extinction rates that are 1,000 to 10,000 times higher than the background rate of species loss.

So what will happen to those plants and animals if and when the climate really starts warming? According to a new study in Nature Climate Change, the answer is pretty simple: they will run out of habitable space, and many of them will die.

The Intergovernmental Panel on Climate Change (IPCC) has estimated that 20% to 30% of species would be at increasingly high risk of extinction if global temperatures rise more than 2˚C to 3˚C above preindustrial levels. Given that temperatures have already gone up by nearly 1˚C, and carbon continues to pile up in the atmosphere, that amount of warming is almost a certainty.

But Rachel Warren and her colleagues at the University of East Anglia (UEA), in England, wanted to know more precisely how that extinction risk intensifies with warming — and whether we might be able to save some species by mitigating climate change. In the Nature Climate Change paper, they found that almost two-thirds of common plants and half of animals could lose more than half their climatic range by 2080 if global warming continues unchecked, with temperatures increasing 4˚C above preindustrial levels by the end of the century. Unsurprisingly, the biggest effects will be felt near the equator, in areas like Central America, Sub-Saharan Africa, the Amazon and Australia, but biodiversity will suffer across the board.

Our research predicts that climate change will greatly reduce the diversity of even very common species found in most parts of the world. This loss of global-scale biodiversity would significantly impoverish the biosphere and the ecosystem services it provides.

We looked at the effect of rising global temperatures, but other symptoms of climate change such as extreme weather events, pests, and diseases mean that our estimates are probably conservative. Animals in particular may decline more as our predictions will be compounded by a loss of food from plants.

The good news is that a much hotter future isn’t a certainty. If global greenhouse-gas emissions peak within the next few years and begin to decline afterward, the UEA researchers suggest that we can preserve many species that would otherwise be lost. Even if the peak is delayed until 2030, fewer species will go extinct. Mitigation will also buy us time to figure out adaptation strategies for some species that are being displaced by climate change.

Of course, there’s virtually no chance that global emissions will peak within the next few years — and odds aren’t much better even if we give ourselves another 15 years. Even if we can curb warming, an expanding and (hopefully) richer human population is going to put more and more pressure on what we once quaintly called the natural world. The future is going to be difficult for a lot of nonhumans — and tough for a lot of humans too. But a crowded world is a better bet than a hot and crowded one.